On Friendly Index Sets of Spiders

Let G be a graph with vertex set V(G) and edge set E(G), and let A be an abelian group. A labeling f : V (G)-> A induces an edge labeling f* : E(G)-> A defined by f*(xy) = f(x)+ f(y), for each edge xy is an element of E(G). For i is an element of A, let v(f) (i) = vertical bar{v is an element of V(G) : f(v) = i}vertical bar and e(f) (i) = vertical bar{e is an element of E(G) : f*(e) = i}vertical bar. Let c(f) = {vertical bar e(f) (i) - e(f) (j)vertical bar : (i, j) is an element of A x A}. A labeling f of a graph G is said to be A-friendly if vertical bar v(f)(i) - v(f) (j)vertical bar <= 1 for all (i, j) is an element of A x A. If c(f) is a (0, 1)-matrix for an A-friendly labeling f, then f is said to be A-cordial. When A = Z(2), the friendly index set of the graph G, FI(G), is defined as {vertical bar e(f) (0) - e(f)(0)vertical bar: the vertex labeling f is Z(2)-friendly}. In this paper, we determined the friendly index sets of many spiders.